Verdict
Call
12 outs, flop, third-pot bet
- Chance to hit by the rivertwo cards to come44.96%
- Equity the call needs$33.33 into a pot of $166.6720.00%
- Margin over the priceyour chance minus the price+24.96 points
Chance against price
44.96% against 20.00%: the draw beats the price by 24.96 points. On this flop against a third-pot bet, that is a comfortable call.
Count a flush draw with a gutshot and you land on 12 outs. With 47 cards unseen, the next card helps 25.53% of the time.
The same spot in dollars
- The pot before betting$100
- Your opponent bets$33.33
- Cost to call$33.33
- Total pot after calling$166.67
- Gain on a hit$133.33
- Net loss when you miss$33.33
- Probability of a hit44.96%
- Expected value of calling+$41.60
- Equity needed to break even20.00%
- Exact margin over the price+24.9584 points
- Outs that exactly reach the price4.91 outs
- Margin measured in outs+7.09 outs
Suppose a hit wins the entire pot, a miss loses your call, and no more betting follows. The average gain is $59.94, the average loss is $18.35, and calling gains $41.60 on average, or +1.248 per dollar called.
As odds, 1.22 : 1 against hitting meets pot odds of 4 : 1.
Watch the pot you divide by. Leaving your call out turns 20.00% into 25.00%, and the margin into +19.9584 points. Dividing by the starting pot gives 33.33% and a margin of +11.6250 points, further from the truth.
How much room the call has
If some outs turned out to be shared with a better hand, you could give up 7 outs and still call. The floor is 5, at 20.35%.
The call keeps its edge until you lose $92.52 on later streets after hitting. That is 2.78 times the $33.33 you pay now.
| Given back later | Price with it | Your chance minus price | Value of the call | Call? |
|---|---|---|---|---|
| $0 | 20.00% | +24.96 points | +$41.60 | Call |
| $10 | 21.28% | +23.68 points | +$37.10 | Call |
| $25 | 23.53% | +21.43 points | +$30.36 | Call |
| $50 | 28.57% | +16.39 points | +$19.12 | Call |
| $100 | 50.00% | -5.04 points | -$3.36 | Fold |
One card or two
Whether you count one card or two, the answer is a call. The river figure is 44.96%, the next-card figure is 25.53%, and both are measured against 20.00%.
| Cards counted | Chance | Margin over price | Value of the call | Verdict |
|---|---|---|---|---|
| By the river, two cards | 44.96% | +24.9584 points | +$41.60 | Call |
| Next card only | 25.53% | +5.5319 points | +$9.22 | Call |
The call as outs change
Here are the neighbors of 12 outs, priced against the same 20.00%. One more out lifts your chance by about 3.15 points.
The draw across every bet size
Bigger bets ask for more equity while your chance stays at 44.96%. Here is every bet size against the same draw, with the row for this page marked.
Your 44.96% chance tops every price in the table, so every bet size is a call: the largest price, 44.44%, is still below it.
| Bet size | Equity needed | Margin | Verdict |
|---|---|---|---|
| quarter-pot | 16.67% | +28.29 points | Call |
| third-pot, this page | 20.00% | +24.96 points | Call |
| two-fifths-pot | 22.22% | +22.74 points | Call |
| half-pot | 25.00% | +19.96 points | Call |
| two-thirds-pot | 28.57% | +16.39 points | Call |
| three-quarter-pot | 30.00% | +14.96 points | Call |
| pot-size | 33.33% | +11.63 points | Call |
| 1.25x-pot | 35.71% | +9.24 points | Call |
| 1.5x-pot | 37.50% | +7.46 points | Call |
| 2x-pot | 40.00% | +4.96 points | Call |
| 3x-pot | 42.86% | +2.10 points | Call |
| 4x-pot | 44.44% | +0.51 points | Call |
How this is computed
Here is how 44.96% was found. Deal every pair of the 47 unseen cards: 595 of 1,081 pairs contain no out.
Four assumptions sit behind the verdict: you call the full bet, a hit wins the entire pot, no money goes in after the call, and every one of the 47 unseen cards is equally likely. The price is $33.33 / $166.67 = 20.00%. No card is taken out for what an opponent might hold.
Computed from the closed form by the GeorgeLiPoker math library.
Updated
Questions
Call or fold with 12 outs on the flop against a bet of a third of the pot?
Verdict: call. A third-pot bet asks for 20.00% and you have 44.96%, a margin of +24.96 points. For a $33.33 call into a $100 pot, with no later bets and the whole pot won on a hit, the average is +$41.60.
How many outs make a call correct against a third of the pot on the flop?
5 outs is the line. At 5 the chance is 20.35%, enough for 20.00%; one fewer gives 16.47%, which is not. Your 12 outs sit 7 above it on the flop, at 44.96%.
One card or two: which number belongs next to the 20.00% price?
Match the number to the betting: 44.96% if all-in or checked down, 25.53% if you face another bet on the turn. The price is 20.00%, and both numbers agree on call.
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